Femtosecond laser direct writing is a recently developed technique to fabricate optical waveguides. An overview of the technique can be conveniently found in G. Della Valle, R. Osellame & P. Laporta Journal of Optics A: Pure and Applied Optics 11, 013001 (2009). According to this technique, ultrafast laser pulses are focused in the bulk of a transparent substrate by means of a microscope objective, where non-linear absorption phenomena (multi-photon absorption, avalanche processes . . . ) induce a permanent modification of the material, localized in the focal region. In particular, by properly tuning the irradiation parameters, a localized refractive index increase can be obtained: by translating the substrate with respect to the laser beam, it is possible to literally draw the waveguides inside the material. Since no lithographic masks are employed, this technology enables quick and low-cost prototyping of novel photonic devices. In addition, since the waveguide is directly written in the volume of the substrate, this is the only technique which allows one to easily realize optical circuits with three-dimensional layouts.
A more detailed discussion of the interaction of a laser pulse with a duration of tens or hundreds of femtoseconds, focused by a lens or an objective inside a dielectric substrate, transparent at the wavelength of the laser beam (e.g. an Yb:based femtosecond laser system, with λ=1030 nm wavelength, and a borosilicate glass substrate) is provided below.
The photon energy Eph=hc/λ, at this wavelength, falls into the transparency bandgap of the material (Eph<Egap), thus the commonly considered linear absorption phenomena are not efficient. The simultaneous absorption of n photons, to give nEph≧Egap, which has a generally lower probability, may however occur in this case. Then, the energy absorbed from a beam of intensity I becomes proportional to In, i.e. it is non-linear with the intensity. Such non-linear absorption phenomena are negligible at low intensity but become relevant at the high peak intensity of femtosecond pulses, especially if the intensity is further increased by focusing the beam with a lens or an objective.
In particular, in the case of a pulse duration of some hundreds of femtoseconds, the typical interaction process between the focused laser pulse and the transparent dielectric substrate is composed of a few steps:                I. in the first part of the pulse (with reference to the time evolution), a seed of free electrons is created by multi-photon absorption processes, triggered by the high intensity,        II. such free-electron seed is multiplied by avalanche ionization processes; a cloud of plasma with increasing density is generated,        III. at a certain point in this process the plasma density reaches a level for which the laser wavelength is absorbed linearly by the plasma; the remaining part of the laser pulse is then absorbed linearly by the plasma cloud,        IV. once the laser pulse has ended, the highly energetic cloud of plasma transfers the energy to the substrate lattice in a relaxation process, producing a permanent modification.        
An important consequence of the non-linearity of the interaction process of the focused beam is that the multi-photon absorption, the plasma generation and the subsequent permanent modification of the material occur only localized around the focal region, where the highest intensity is reached. It is thus made possible to induce in this way a localized modification in the bulk of a transparent material without affecting the external surface or other regions of the substrate.
Depending on the pulse energy, different modification types can be observed (with influence also from the specific substrate and from other irradiation parameters). Generally, for high energy levels material damage and microexplosions are reported. For lower energy levels and by properly tuning the irradiation parameters, a lighter (but still permanent) modification can be observed, namely a localized refractive index increase, in which the substrate maintains its transparency optical properties.
WO 2001/44871 by Corning Incorporated describes a method for realizing a guiding path, such as a waveguide, in a dielectric substrate. The substrate may consist, for instance, of borosilicate glass, sulfide glass or crystalline material. A pulsed laser beam is focused into the substrate, while the focus is translated with respect to it along a scanning path; the translation speed is tuned to obtain a refractive index increase of the material along the scanned path. No physical damage occurs to the material because of the laser irradiation. By means of this method several optical devices may be realized.
It is desirable to control the polarization of the light propagating inside an optical waveguide. It is notably difficult to realize waveguide-integrated polarization rotators. On the one side, lithographic waveguides generally yield enough birefringence to prevent cross-talk between different polarization modes; on the other side, a rotation of the waveguide birefringence axis requires to alter the waveguide symmetry, which is not trivial with planar technologies.
Different kinds of polarization rotators are reported, fabricated by lithographic techniques. In a first case, only a slight alteration of the waveguide symmetry is induced, either by depositing asymmetric structures above the waveguide (see e.g. Y. Shani et al., Applied Physics Letters 59, 1278-1280 (1991)), or by directly realizing a slightly asymmetric waveguide core cross-section (see e.g. H. Heidrich et al., IEEE Photonics Technology Letters 4, 34-36 (1992)). In this category of devices the two polarization modes are only slightly hybridized: to obtain a full polarization rotation several waveguide sections, alternately with a symmetric and asymmetric cross-section, need to be cascaded. In a third case, a single waveguide segment with pronounced cross-section asymmetry is sufficient to induce a full polarization rotation (J. Huang et al., IEEE Photonics Technology Letters 12, 317-319 (2000)). However, all these architectures, besides suffering from additional losses due to abrupt changes in the waveguide cross-section along the propagation (which become increasingly relevant when the number of cascaded segments increases), the fabrication of asymmetric waveguides or collateral deposition processes require additional lithographic steps, with all the problems related to the alignment precision between different steps. A further class of polarization rotators exploit a multi-mode waveguide segment (K. Mertens et al., IEEE Photonics Technology Letters 10, 388-390 (1998)), in which T.E. and T.M. modes are highly hybridized and power is transferred from one polarization to the other. Although the number of lithographic steps required in the latter case may be smaller than in the previously discussed architectures, it is in all cases true that the design of these devices needs the support of complex numerical simulations and that strict fabrication tolerances are required.
Hence, on the one hand, conventional lithographic techniques enable one to fabricate waveguide-integrated polarization rotators at the price of a remarkable increase in the complexity of the fabrication process. On the other hand, integrated birefringent waveplates which perform a polarization rotation have not been demonstrated yet, by means of direct writing fabrication techniques.
In the context of femtosecond laser micromachining, a fine control on the modal birefringence has been indeed demonstrated for waveguides fabricated in fused silica substrate, either by [[a]] varying the laser irradiation parameters (L. Fernandes et al., Optics Express 19, 18294-18301 (2011)) or by inscribing collateral structures in the substrate, which induce additional mechanical stress around the waveguide (L. Fernandes et al., Optics Express 20, 24103-24114 (2012)). However, the direction of the birefringence axis remains fixed and does not change the tilt angle. The possibility to modify this direction is indeed essential in order to effectively manipulate the polarization of the light propagating in waveguide circuits.